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MathGroup Archive 1995

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Re: Base 10 to Base 2 conversion error ?

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1778] Re: Base 10 to Base 2 conversion error ?
  • From: dchua at abel.math.harvard.edu (David Chua)
  • Date: Sun, 30 Jul 1995 21:33:43 -0400
  • Organization: Anarchists Inc.

>Well, there are only 100^2 cases, so it's fairly easy to write a 
>mathematica notebook that will mechanically test all cases.  It may take 
>all night to run, but you won't need to catch a mathematician.

  Whoa! Just see if 0.01 works, which it doesn't. You need 2^(-n) to
  divide 0.01 for some positive integer n.  (To see this: Flip things
  over and the condition is 100 be a factor of 2^n, which won't happen
  since powers of 2 end in 2, 4, 6 or 8; never 0.)

>Is it really necessary to be accurate to the penny?  Why isn't one part 
>in a billion accurate enough?

  Even if they're playing with billions of dollars, I would think that
  Mathematica can use enough precision to prevent money loss. 

  Hope this helps.



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